Final answer:
The intertemporal budget set can be represented graphically as a line with vertices showing the consumption possibilities across two periods with varying interest rates for saving and borrowing. The slope of the line changes based on the rate of return, demonstrating the impact on future consumption.
Step-by-step explanation:
The question is asking us to illustrate the intertemporal budget set of an individual with different incomes in two periods, facing varying interest rates for saving and borrowing. When graphing this on consumption in period one (c1) and consumption in period two (c2), we must take into account the differing interest rates for savings and for borrowing.
If the individual saves money in the first period at an interest rate of 5%, the future value of the savings will be higher than the initial amount saved. Conversely, if the individual needs to borrow money, they face a 10% interest rate, resulting in less consumption possible in the second period. The budget set will be represented by a line with vertices that reflect the maximum consumption in each period if all income is spent in one period, as well as the consumption possibilities if income is saved or borrowed between the two periods.
To graph this, we would plot the individual's income in the first and second periods on the axes (c1 and c2). The point where the individual spends all income in period 1 would be (20,000, 0) on the graph, assuming no savings. If all income from the first period is saved at a 5% interest rate, the future value of this income would increase the consumption possibility in period 2. This would shift the point upwards on the c2 axis, forming the upward pivot of our budget line due to savings. Conversely, borrowing would pivot the budget line downwards, since borrowing results in less consumption in period 2 due to the higher interest rate of 10%.
An example of the effects of changing interest rates can be seen through Yelberton's choices in the question's context. When his rate of return increases, the future value of his savings increases significantly, as noted by a compounded amount after 30 years. This illustrates the power of compound interest and how changes in the rate of return affect an individual's intertemporal budget constraint and decisions on present and future consumption.